11,392 reputation
164133
bio website linkedin.com/in/nikov
location Redmond, WA
age 35
visits member for 3 years, 2 months
seen Jan 20 at 1:38

Having more than 12 years of experience in software development and testing, I currently work as SDE 2 at Microsoft on the ".NET Compiler Platform" project (a.k.a. "Roslyn") — the next generation of managed C# and VB.NET compilers, programming language tools and IDE. Among other things, my job involves participation in design of type systems and new language features, checking them for soundness and their actual implementation and testing.

I am also a member of TC49-TG2 (Ecma standardization committee for C#), currently working on the next version of the international standard Ecma-334.

Although I am not a professional mathematician, I hold a degree in theoretical physics, and I am very passionate about mathematics, especially about evaluation of integrals, sums and products in a closed form, foundations of mathematics, order theory, type theory, computability theory, graph theory and combinatorics.

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Feel free to contact me at <ɯoɔ·ןᴉɐɯᵷ(ʇɐ)ʌoʞᴉuʇǝɥsǝɹ·ʌ>


Jan
11
comment Closed form for ${\large\int}_0^\infty\frac{x-\sin x}{\left(e^x-1\right)x^2}\,dx$
It looks like the red sum can be simplified using robjohn's answer to another Laila's question, and using $\prod_{n\ge1}\left(1+n^{-2}\right)=\frac{\sinh\pi}{\pi}$.
Jan
11
comment Is there a domain “larger” than (i.e., a supserset of) the complex number domain?
To be precise, surreal numbers do not form a set, but they are a proper class.
Dec
26
comment A closed-form of product the gamma functions containing $\pi$ and $\phi$
@Anastasiya-Romanova秀 You might want to read this paper: Expressions for values of the gamma function by Raimundas Vidūnas.
Dec
25
comment A closed form for the series $\sum_{n=1}^{\infty} \frac{H_n^2-(\gamma + \ln n)^2}{n}$
@OlivierOloa Could you please post an explicit result for $m=3$?
Dec
24
comment A closed form for the series $\sum_{n=1}^{\infty} \frac{H_n^2-(\gamma + \ln n)^2}{n}$
@OlivierOloa Have you been able to find or conjecture values of $\sum_{n=1}^{\infty} \dfrac{H_n^m-(\gamma + \ln n)^m}{n}$ for $m>2$?
Dec
24
comment From the series $\sum_{n=1}^{+ \infty} \left(H_{n}-\ln n-\gamma -\frac{1}{2n}\right)$ to $\zeta(\frac{1}{2}+it)$
It looks like for $\alpha\in\mathbb Q$ the last integral has a form $p+q\ln\alpha+\pi\tau$, where $p,q\in\mathbb Q$, and $\tau$ is an algebraic number. I could not find general expressions for those coefficients.
Dec
20
awarded  Constituent
Dec
16
comment Existence and uniqueness of a function generalizing a finite sum of powers of logarithms
Actually, for $x\in\mathbb N$ and any $a>0$ the fractional derivative assumes correct values (a finine sum of powers of logarithms), so it satifies the first condition and the second condition for integer arguments. Can we prove that it actually satisfies the second conditions for all real $x>1$, and that it is a convex and analytic function?
Dec
16
comment Existence and uniqueness of a function generalizing a finite sum of powers of logarithms
Yes, I tried, but I could not obtain any explicit form (or any form suitable for a numeric approximation) for the fractional derivative, neither I proved that it would yield the desired result (i.e. that all conditions in the problem statement would be satisfied).
Dec
16
comment Existence and uniqueness of a function generalizing a finite sum of powers of logarithms
Yes, for $a\in\mathbb N$ it does (although I haven't proved its uniqueness). But how to make sense of $\zeta^{(a)}$ for fractional $a$?
Dec
16
revised Existence and uniqueness of a function generalizing a finite sum of powers of logarithms
added 9 characters in body
Dec
16
asked Existence and uniqueness of a function generalizing a finite sum of powers of logarithms
Dec
11
awarded  Nice Question
Dec
8
awarded  Caucus
Dec
8
revised A couple of definite integrals related to Stieltjes constants
added 178 characters in body
Dec
8
comment A couple of definite integrals related to Stieltjes constants
@Anastasiya-Romanova Because we know a value of a linear combination of two integrals, it's enough if we find a value of any of them (we would get the other one for free). Do you know a value of any of them?
Dec
8
asked A couple of definite integrals related to Stieltjes constants
Nov
17
awarded  Yearling
Nov
17
awarded  Good Question
Nov
14
awarded  Nice Question